# Measurement

Measurements are ways that we tell others how much of an item we have. There are
two systems of measuring things—English and Metric. English measurements are used
only in the United States, while metric measurements are used in nearly every other
country. Measurements are used to give number values to distance (length, width,
and height), weight, time, volume (liquid measurements), and temperature.

To get you used to these measurements, we’re providing a list of commonly used English
and metric measurements, and their equivalents.

## Common English Measures

 Distance Inches (in) 12 in = 1 ft Feet (ft) 3 ft = 1 yd Yards (yd) 1760 yd = 1 mi Miles (mi) 1 mi = 5280 ft Weight Ounces (oz) 16 oz = 1 lb Pounds (lb) 2000 lb = 1 t Tons (t) 1 t = 2000 lb Volume Teaspoons (tsp) 3 tsp = 1 tbsp Tablespoons (tbsp) 1 tbsp = 3 tsp Fluid ounces (fl oz) 8 fl oz = 1 cup Cups (c) 2 cups = 1 pt Pints (pt) 2pt = 1qt, 8 pt = 1 gal Quarts (qt) 4 qt = 1 gal Gallons (gal) 2 gal = 1 peck Pecks 4 pecks = 1 bushel Bushels 1 bushel = 4 pecks Temperature Degrees Fahrenheit (°F) Speed Miles per hour (mph)

## Common Metric Measures

The metric system is also divided into different categories of measurement, but
it has a base unit for each category. A base unit means that that is what the category
is usually (but not always) measured in, and all the other terms of measurement
in that category are built from the base unit.

 Distance Millimeter (mm) 1000 mm = 1 m Centimeter (cm) 100 cm = 1 m Meter (m) base unit (1) Kilometer (km) 1000 m = 1 km Weight Milligrams (mg) 1000 mg = 1 g Grams (g) base unit (1) Kilograms (kg) 1000g = 1 kg, 1000 kg = 1 t Metric ton (t) 1000 kg = 1 t Volume Milliliters (mL) 1000 mL = 1 L Liters (L) base unit (1) Temperature Degrees Celsius (°C) Speed Meters per second (m/s)

## Universal Measures

 Time Seconds (sec) 60 sec = 1 min Minutes (min) 60 min = 1 hr Hours (hr) 24 hr = 1 day Days 7 days = 1 wk Weeks (wk) (about) 4 wk = 1 mo Months (mo) 12 mo = 1 yr Years (yr) 1 yr = 365 days Decades 1 decade = 10 yr Centuries 1 century = 100 yr Millennium 1 millennium = 1000 yr

## Metric Prefixes

There are metric prefixes that you should memorize in order to help you determine
metric measurements. They are, from smallest to largest:

 Nano n 10^-9 0.000000001 1/1000000000 Micro u 10^-6 0.000001 1/1000000 Milli m 10^-3 0.001 1/1000 Centi c 10^-2 0.01 1/100 Deci d 10^-1 0.1 1/10 Base unit – – – – Deka da 10 10 Hecto h 10^2 100 Kilo k 10^3 1000 Mega M 10^6 1000000 Giga G 10^9 1000000000 Tera T 10^12 1000000000000

Each of these prefixes would go in front of a base unit. Take, for example, length.
The base unit for length is the meter. However, we could put a larger prefix, like
kilo, in front of it: kilometer (km). Now, it means 1000 meters, because kilo means
1000. We could also put a smaller prefix on it, such as centimeter (cm). Now, it
means 1/100 of a meter, or .01 meter.

You also might notice that all of the metric prefixes are multiples of 10 (1, 10,
100, 1000, etc). This makes converting from one to the other far easier than English
measures, because you are always multiplying or dividing by 10; remember, multiplying
and dividing by 10 simply involves moving the decimal.

## English to English Conversions

Most often, if you live in the US, you will be performing English to English conversions
between measurements. Converting involves multiplying or dividing by a conversion
factor, most of which are listed above. When you are going from smaller units to
larger units, you would divide, and when you are going from larger to smaller units,
you multiply.

For example, if you wanted to convert days to hours, you would first stop and think:
which is larger, a day or an hour? A day is larger, so you would think, how would
one convert from larger to smaller units? Well, as we said, larger to smaller units
is when you multiply, so you would multiply by the conversion factor, which is 24
since there are 24 hours in 1 day.

The actual problem would look like this: Convert 3 days to hours.

3 days x 24 hours = 72 hours

We would use 24 hours because are 24 hours per every one day, and right now we have
3 days that we want to convert to hours. Converting back would look like the opposite.
For example: Convert 72 hours to days.

72 hours / 24 hours = 3 days

Here, we used 24 hours again, because we know there are 24 hours in every 1 day,
and we want to see how many days we’ll have if we have 72 hours.

Let’s practice this some more. Convert 3 yards into feet.

First, think “which is larger, yards or feet?”

Realize that yards are larger than feet, so you are converting from larger to smaller.
This indicates multiplication.

Find the conversion factor—3 feet in 1 yard. Therefore, you’ll be multiplying by
3.

You can set it up like this: 3 yards x 3 feet = 9 feet

We use 3 feet because there are 3 feet in every yard, and we want to find out how
many feet are in 3 yards. Thus, our final answer is 9 feet.

When using conversions, you have to make sure that you are converting to another
unit within the same area. For example, so far we have converted units of time (days
to hours, and vice versa) and then we converted units of distance (yards to feet),
and this is normal. There is no way, however, to convert from days to yards, or
from pounds to degrees Fahrenheit, and so on. If you start with distance, you must
end with distance; if you start with time, you must end with time, and so on.

Here are a few problems for you to try.

Convert 4 lbs into ounces.

A.
64 lb
B.
8 oz
C.
16 oz
D.
64 oz

The correct answer here would be D.

First, determine whether you are converting from larger to smaller units or from
smaller to larger units. You can determine that a pound is larger than an ounce,
so you are going from larger to smaller; this indicates multiplication. You find
the conversion unit, and see that there are 16 oz in 1 lb. Thus, the conversion
would look like this:

4 lb x 16 oz = 64 oz

We use 16 oz because there are 16 oz in every 1 lb, and we want to figure out how
many oz are in 4 lb. Thus, our final answer is 64 oz.

Convert 16 pecks into bushels.

A.
4 pecks
B.
4 bushels
C.
64 pecks
D.
64 bushels

The correct answer here would be B.

First, determine whether you are converting from larger to smaller units or from
smaller to larger units. You can determine that a peck is smaller than a bushel,
so you are going from smaller to larger; this indicates division. You find the conversion
unit, and see that there are 4 pecks in 1 bushel. Thus, the conversion would look
like this:

16 pecks / 4 pecks = 4 bushels

We use 4 pecks because there are 4 pecks in every 1 bushel, and we want to figure
out how many bushels we would have if we had 16 pecks. Thus, our final answer is
4 bushels.

Now, we’re going to show you how to do harder conversions. Sometimes, the conversions
will not come out evenly, as the previous ones did. For example, you may have the
following problem:

Convert 2 days and 5 hours into hours.

This simple conversion problem just became a two step problem. The first step is
to convert the days into hours, as normal. The second step is to add the converted
days to the already existing hours. So, you would do the following:

2 days x 24 hours = 48 hours, because you are converting from larger to smaller,
so you multiply.

48 hours + 5 hours = 53 hours. You add the two together because the problem gave

Let’s try one more harder problem.

Convert 6 days 16 hours and 34 minutes into minutes.

Once again, this is a 3 step conversion problem. First, you’ll be converting 6 days
into hours, then into minutes since there is no direct conversion from days to minutes.
Then, you’ll be converting 16 hours into minutes. Then you’ll be adding the three
numbers together, in inches, to get your final answer. The work would look like
this:

Determine if you’re working with units that are being converted from smaller to
larger, or from larger to smaller. You’ll see that in both cases, days and hours,
both are larger than minutes. Thus, for each conversion, you will use multiplication
as you’re going from larger to smaller. Here are your conversions:

6 d x 24 hr = 144 hr
144 hr x 60 min = 8640 min
16 hr x 60 min = 960 min
8640 min + 960 min + 34 min = 9634 min

In the first conversion, we used 24 hours because there are 24 hours in a day. We
had to convert days to hours before we could convert hours to minutes. The second
conversion shows the hours from the previous conversion being changed into minutes.
The third conversion shows the hours the problem gave being converted into minutes.
The last step shows the three numbers being added together, resulting in the grand
total of minutes, which amounted to 9634 minutes.

Now, we’ll have a harder one for you to try. Convert 4 gallon 3 quarts 1 pints into
pints.

A.
16 qt
B.
32 pt
C.
38 pt
D.
39 pt

The correct answer here would be D.

This too is a 3-step conversion problem. First, you’ll be converting 4 gallons into
quarts, then into pints. Then, you’ll be converting 3 quarts into pints. Last, you’ll
would look like this:

Determine if you’re working with units that are being converted from smaller to
larger, or from larger to smaller. You’ll see that in both cases, gallons and quarts,
both are larger than pints. Thus, for each conversion, you will use multiplication
as you’re going from larger to smaller. Here are your conversions:

4 gal x 4 qt = 16 qt
16 qt x 2 pt = 32 pt

3 qt x 2 pt = 6 pt
32 pt + 6 pt + 1 pt = 39 pt

In the first conversion, we used 4 quarts because there are 4 quarts in 1 gallon.
We had to convert gallons to quarts before we could convert to pints. The second
conversion shows the quarts from the previous version being changed into pints.
The third conversion shows the quarts the problem gave being converted into pints.
The last step shows the three numbers being added together, resulting in the grand
total of pints, which amounted to 39 pints.

## Metric to Metric Conversions

Metric to metric conversions are less common—but easier to perform—than English
to English conversions. The metric system is based on powers of ten, meaning 10,
100, 1000, 10000, 100000 and so on.

The same rules for conversions still apply when you’re doing metric to metric conversions
as do English to English conversions. For example, larger to smaller units still
multiply and smaller to larger units still divide. The only change is in the conversion
units; instead of being random, now they are all powers of ten.

Let’s try an example of this. Convert 3 meters to centimeters.

First, think: which is larger, a meter or a centimeter? You would conclude that
a meter is larger than a centimeter. Therefore, we are going to multiply by the
conversion factor. You would look in the table above for the conversion factor from
m to cm, and see that there are 100 cm in a m, so you’d be multiplying by 100.

The actual problem looks like this:

3 m x 100 cm = 300 cm

We would use 100 cm as our conversion factor, because there are 100 cm in 1 m. Thus,
our final answer is 300 cm.

We’ll do one more before we give you a few to try on your own. This time, convert
2000 grams into kilograms.

First, think: which is larger, a kilogram or a gram? You would conclude that a gram
is smaller than a kilogram. Therefore, we are going to divide by the conversion
factor. You would look in the table above for the conversion factor from g to kg,
and see that there are 1000 g in a kg, so you’d be dividing by 1000. Here’s the
work:

2000g / 1000g = 2 kg

We use 1000 g because there are 1000 grams in a kilogram. Thus, our final answer
is 2 kg.

Now, you can try one.

Convert 10,000 milliliters to liters.

A.
10 L
B.
100 L
C.
1000 L
D.
1 L

The correct answer here would be A.

First, think: which is larger, a milliliter or a liter? You would conclude that
a milliliter is smaller than a liter. Therefore, we are going to divide by the conversion
factor. In order to find the conversion factor, you would look in the table above,
and see that there are 1000 mL in a L, so you’d be dividing by 1000. Here’s the
work:

10,000 mL / 1,000 mL = 10 L

We use 1,000 mL because there are 1,000 mL in one liter. Thus, our final answer
is 10 L.

## English to Metric Conversions

Here is a conversion chart of many of the common English to metric conversions.
English measures are on the left and metric measures are on the right.

 Distance 1 inch = 2.54 cm 1 foot = 0.3 meters 1 yard = 0.9 meters 1 mile = 1.6 kilometers Weight 1 ounce = 28.4 grams 1 pound = 0.5 kilograms Volume 1 teaspoon = 4.9 milliliters 1 cup = 237 milliliters 1 pint = 473 milliliters 1 quart = 0.9 liters 1 gallon = 3.79 liters

Temperature

To convert from degrees C to degrees F

(deg C x 9/5) + 32

To convert from degrees F to degrees C

(deg F – 32) x 5/9

Now let’s practice converting between the two. Using this chart, if you’re going
from English to metric, you would multiply. If you’re going from metric to English,
you’d divide.

Here are a few examples:

Convert 4 lbs to kg.

First, you know that you’re going from English to metric, so you know you’ll be
multiplying. We know that there are .5 kg in each lb, so we set up our equation
like this:

4 lb x .5kg = 2 kg

Thus, 2 kg is our final answer.

Now, let’s practice going from metric to English.

Convert 200 milliliters to cups.

First, you know that you’re going from metric to English, so you know you’ll be
dividing. We know that there are 237 mL in each cup, so we set up our equation like
this:

200 mL / 237 mL = .84 cups

We use 237 mL because there are 237 mL in a cup. Thus, .84 cups is our final answer.

Notice that we divide when we are moving from metric to English, we divide; when
we move from English to metric, we multiply.

Now, here is one for you to try:

Convert 3.2 miles to kilometers.

A.
5.12 miles
B.
4.8 miles
C.
4.8 kilometers
D.
5.12 kilometers

The correct answer here would be D.

Think: we started out with an English measure, miles, and we want to convert it
to a metric measure, kilometers. We know that, using the table above, we have to
multiply to get from English to metric. So, we’ll set up our equation like this:

3.2 mi x 1.6 km = 5.12 km

We use 1.6 km because there are 1.6 km in a mile. Thus, 5.12 km is our final answer.

## Temperature Conversions

Converting from degrees Fahrenheit to degrees Celsius, and vice versa, involves
using very specific equations, so we’ll show you how to use them so that you don’t
get confused.

To convert from degrees F to degrees C, you take (deg F – 32) x 5/9, then you have
degrees Celsius. For example, let’s say we wanted to convert 32°F into °C. This
is what your set up equation would look like. Our starting number, 32°F is going
to be in blue, and the rest of the equation is in black.

Now, we have to remember to do the part of the equation in parentheses first, then
we do the rest. The part in parenthesis is a subtraction problem, 32 – 32, which
equals 0. Now, the equation looks like this:

Normally, we would multiply our whole number by the fraction, but in this case,
our whole number is 0, and anything times 0 is 0, so we know that our final answer
is 0.

Thus, 32°F = 0°C.

Let’s try one more Fahrenheit to Celsius conversion. This time, we’ll give you the
temperature and you can practice converting it.

Now, our last step is to round our answer to the closest degree. In order to do
this, we look at the first place after the decimal, which is an 8. We know that
8 rounds up, so our 3 becomes a 4, and our final answer is 24°C. (For a review on
how to round, see
Rounding Numbers
).

{24|24 deg|24 deg C|24 degree|24 degree C|24 degrees|24 degrees C|24°C|24°}

Now let’s practice converting from Celsius to Fahrenheit. It’s similar to what we
just did, but the steps are slightly switched around. To convert from Celsius, the
equation is (°C x 9/5) + 32 = °F. We’re going to solve for the following: 200°C
= ?°F

First, we plug the information into the equation, which looks like this:

Then, we continue to solve the equation, making sure to do the parentheses first,
and then the rest of the problem, like this:

Therefore, our final answer is 392°F.

Now, here’s one for you to try.

Convert 50°C into °F.

First, substitute 50°C into the equation, like this:

Then, continue on to solve the rest of the equation, doing parentheses first, and
then the rest of the addition, like this: